Optimal admission control in series production systems with blocking

This article studies the dynamic control of arrivals of multiple job classes in N-stage production systems with finite buffers and blocking after service. A model with multiple processing stages in series is formulated as a Markov decision process and a state definition from the queueing analysis literature is used to simplify the state-space description. This allows several fundamental admission control results from M/M/N and M/M/N/N queueing models as well as tandem models without blocking to be extended to tandem systems with blocking. Specifically, it is shown that the net benefit of admitting a job declines monotonically with the system congestion; thus the decision to admit any job class is based on threshold values of the number of jobs present in the system. Furthermore, conditions under which a job class is always or never admitted, regardless of the state, are derived. The interaction of blocking and admission control is explored by analyzing the effect of blocking on the optimal admission policy and profit. The article concludes with analyses of why extensions including loss and abandonment cannot sustain the monotonicity properties and two surrogate admission rules that may be used in practice but do not account for the blocking effect.